1/3x=15,x=

Solution for 1/3x=15,x= equation:

1/3x=15.x=

We move all terms to the left:

1/3x-(15.x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

1/3x-(+15.x)=0

We get rid of parentheses

1/3x-15.x=0

We multiply all the terms by the denominator


-(15.x)*3x+1=0

We add all the numbers together, and all the variables

-(+15.x)*3x+1=0

We multiply parentheses

-45x^2+1=0

a = -45; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-45)·1
Δ = 180
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{5}}{2*-45}=\frac{0-6\sqrt{5}}{-90}
=-\frac{6\sqrt{5}}{-90}
=-\frac{\sqrt{5}}{-15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{5}}{2*-45}=\frac{0+6\sqrt{5}}{-90}
=\frac{6\sqrt{5}}{-90}
=\frac{\sqrt{5}}{-15}
$